03045nam 2200517 450 991081687240332120210618083341.01-119-68681-41-119-68684-91-119-68685-7(CKB)4100000010013920(MiAaPQ)EBC6001237(CaSebORM)9781786304551(EXLCZ)99410000001001392020200228h20202019 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierAnalysis, modeling and stability of fractional order differential systems 2 the infinite state approach /Jean-Claude Trigeassou, Nezha Maamri1st editionLondon :ISTE Limited[2019]©20191 online resource (409 pages) illustrationsSystems and industrial engineering series1-78630-455-4 Includes bibliographical references and index.This book introduces an original fractional calculus methodology ('the infinite state approach') which is applied to the modeling of fractional order differential equations (FDEs) and systems (FDSs). Its modeling is based on the frequency distributed fractional integrator, while the resulting model corresponds to an integer order and infinite dimension state space representation. This original modeling allows the theoretical concepts of integer order systems to be generalized to fractional systems, with a particular emphasis on a convolution formulation. With this approach, fundamental issues such as system state interpretation and system initialization – long considered to be major theoretical pitfalls – have been solved easily. Although originally introduced for numerical simulation and identification of FDEs, this approach also provides original solutions to many problems such as the initial conditions of fractional derivatives, the uniqueness of FDS transients, formulation of analytical transients, fractional differentiation of functions, state observation and control, definition of fractional energy, and Lyapunov stability analysis of linear and nonlinear fractional order systems. This second volume focuses on the initialization, observation and control of the distributed state, followed by stability analysis of fractional differential systems.Systems and industrial engineering series.Fractional calculusFractional differential equationsFractional integralsFractional calculus.Fractional differential equations.Fractional integrals.515.83Trigeassou Jean-Claude880053Maamri NezhaMiAaPQMiAaPQMiAaPQBOOK9910816872403321Analysis, modeling and stability of fractional order differential systems 24037360UNINA